Yes, you can do that.
As an individual or as a group, you have the right to object to and even challenge a radio station's license during the period when the license is under review for renewal.
But, there's a procedure and the Federal Communications Commission is very particular about the way you go about it, though it it's not very complicated.
Challenging a station's license can really get the station's management's attention. Just the mention of challenging a station's license will most likely put you at the front of the line for a discussion with the station's General Manager. Of course, you shouldn't threaten anyone with this action but it's perfectly acceptable to let management know you understand your options.
Luckily, sometimes just a conversation about your programming concerns can yield real results. But, when something is wrong at a radio station and no one seems to be taking you seriously, you always have the option to take it to the next level. There are two avenues of action: an "Informal Objection" or a "Petition to Deny." I'll explain those in a moment. First, understand how the process begins.
When to Challenge a Radio Station License
According to fcc.gov, all radio station licenses are scheduled to expire between 2011 and 2014. This includes AM, FM, and noncommercial education FM. Station must file an application to renew.
While a station's license is up for renewal, listeners of a radio station may informally object against the renewal or file a petition to deny the renewal.
To see radio broadcast renewal dates by STATE you can download it here.
To see radio broadcast renewal dates by DATE you can download it here.
Local Public Inspection File
Every radio station must keep a local public inspection file. During their renewal period, you may ask to review it. Stations establish reasonable procedures to allow interested parties to do so during regular business hours. Always be courteous and professional in your requests.